Identifier
- St000847: Binary words ⟶ ℤ
Values
=>
0=>1
1=>1
00=>1
01=>1
10=>1
11=>1
000=>1
001=>1
010=>2
011=>1
100=>1
101=>2
110=>1
111=>1
0000=>1
0001=>1
0010=>2
0011=>1
0100=>2
0101=>3
0110=>2
0111=>1
1000=>1
1001=>2
1010=>3
1011=>2
1100=>1
1101=>2
1110=>1
1111=>1
00000=>1
00001=>1
00010=>2
00011=>1
00100=>3
00101=>3
00110=>2
00111=>1
01000=>2
01001=>4
01010=>6
01011=>3
01100=>2
01101=>4
01110=>2
01111=>1
10000=>1
10001=>2
10010=>4
10011=>2
10100=>3
10101=>6
10110=>4
10111=>2
11000=>1
11001=>2
11010=>3
11011=>3
11100=>1
11101=>2
11110=>1
11111=>1
000000=>1
000001=>1
000010=>2
000011=>1
000100=>3
000101=>3
000110=>2
000111=>1
001000=>3
001001=>5
001010=>7
001011=>3
001100=>3
001101=>4
001110=>2
001111=>1
010000=>2
010001=>4
010010=>8
010011=>4
010100=>7
010101=>11
010110=>7
010111=>3
011000=>2
011001=>5
011010=>7
011011=>5
011100=>2
011101=>4
011110=>2
011111=>1
100000=>1
100001=>2
100010=>4
100011=>2
100100=>5
100101=>7
100110=>5
100111=>2
101000=>3
101001=>7
101010=>11
101011=>7
101100=>4
101101=>8
101110=>4
101111=>2
110000=>1
110001=>2
110010=>4
110011=>3
110100=>3
110101=>7
110110=>5
110111=>3
111000=>1
111001=>2
111010=>3
111011=>3
111100=>1
111101=>2
111110=>1
111111=>1
0000000=>1
0000001=>1
0000010=>2
0000011=>1
0000100=>3
0000101=>3
0000110=>2
0000111=>1
0001000=>4
0001001=>5
0001010=>7
0001011=>3
0001100=>3
0001101=>4
0001110=>2
0001111=>1
0010000=>3
0010001=>6
0010010=>11
0010011=>5
0010100=>10
0010101=>13
0010110=>8
0010111=>3
0011000=>3
0011001=>7
0011010=>9
0011011=>5
0011100=>3
0011101=>4
0011110=>2
0011111=>1
0100000=>2
0100001=>4
0100010=>9
0100011=>4
0100100=>11
0100101=>15
0100110=>10
0100111=>4
0101000=>7
0101001=>16
0101010=>24
0101011=>13
0101100=>9
0101101=>15
0101110=>7
0101111=>3
0110000=>2
0110001=>5
0110010=>10
0110011=>7
0110100=>8
0110101=>16
0110110=>11
0110111=>5
0111000=>2
0111001=>5
0111010=>7
0111011=>6
0111100=>2
0111101=>4
0111110=>2
0111111=>1
1000000=>1
1000001=>2
1000010=>4
1000011=>2
1000100=>6
1000101=>7
1000110=>5
1000111=>2
1001000=>5
1001001=>11
1001010=>16
1001011=>8
1001100=>7
1001101=>10
1001110=>5
1001111=>2
1010000=>3
1010001=>7
1010010=>15
1010011=>9
1010100=>13
1010101=>24
1010110=>16
1010111=>7
1011000=>4
1011001=>10
1011010=>15
1011011=>11
1011100=>4
1011101=>9
1011110=>4
1011111=>2
1100000=>1
1100001=>2
1100010=>4
1100011=>3
1100100=>5
1100101=>9
1100110=>7
1100111=>3
1101000=>3
1101001=>8
1101010=>13
1101011=>10
1101100=>5
1101101=>11
1101110=>6
1101111=>3
1110000=>1
1110001=>2
1110010=>4
1110011=>3
1110100=>3
1110101=>7
1110110=>5
1110111=>4
1111000=>1
1111001=>2
1111010=>3
1111011=>3
1111100=>1
1111101=>2
1111110=>1
1111111=>1
00000000=>1
00000001=>1
00000010=>2
00000011=>1
00000100=>3
00000101=>3
00000110=>2
00000111=>1
00001000=>4
00001001=>5
00001010=>7
00001011=>3
00001100=>3
00001101=>4
00001110=>2
00001111=>1
00010000=>4
00010001=>7
00010010=>12
00010011=>5
00010100=>11
00010101=>13
00010110=>8
00010111=>3
00011000=>4
00011001=>7
00011010=>9
00011011=>5
00011100=>3
00011101=>4
00011110=>2
00011111=>1
00100000=>3
00100001=>6
00100010=>13
00100011=>6
00100100=>16
00100101=>20
00100110=>13
00100111=>5
00101000=>11
00101001=>22
00101010=>31
00101011=>15
00101100=>12
00101101=>17
00101110=>8
00101111=>3
00110000=>3
00110001=>8
00110010=>15
00110011=>9
00110100=>12
00110101=>20
00110110=>13
00110111=>5
00111000=>3
00111001=>7
00111010=>9
00111011=>6
00111100=>3
00111101=>4
00111110=>2
00111111=>1
01000000=>2
01000001=>4
01000010=>9
01000011=>4
01000100=>13
01000101=>16
01000110=>11
01000111=>4
01001000=>12
01001001=>24
01001010=>35
01001011=>17
01001100=>15
01001101=>21
01001110=>10
01001111=>4
01010000=>7
01010001=>17
01010010=>35
01010011=>20
01010100=>31
01010101=>51
01010110=>33
01010111=>13
01011000=>9
01011001=>23
01011010=>32
01011011=>20
01011100=>9
01011101=>16
01011110=>7
01011111=>3
01100000=>2
01100001=>5
01100010=>11
01100011=>7
01100100=>13
01100101=>23
01100110=>17
01100111=>7
01101000=>8
01101001=>21
01101010=>33
01101011=>22
01101100=>13
01101101=>24
01101110=>12
01101111=>5
01110000=>2
01110001=>5
01110010=>10
01110011=>8
01110100=>8
01110101=>17
01110110=>12
01110111=>7
01111000=>2
01111001=>5
01111010=>7
01111011=>6
01111100=>2
01111101=>4
01111110=>2
01111111=>1
10000000=>1
10000001=>2
10000010=>4
10000011=>2
10000100=>6
10000101=>7
10000110=>5
10000111=>2
10001000=>7
10001001=>12
10001010=>17
10001011=>8
10001100=>8
10001101=>10
10001110=>5
10001111=>2
10010000=>5
10010001=>12
10010010=>24
10010011=>13
10010100=>22
10010101=>33
10010110=>21
10010111=>8
10011000=>7
10011001=>17
10011010=>23
10011011=>13
10011100=>7
10011101=>11
10011110=>5
10011111=>2
10100000=>3
10100001=>7
10100010=>16
10100011=>9
10100100=>20
10100101=>32
10100110=>23
10100111=>9
10101000=>13
10101001=>33
10101010=>51
10101011=>31
10101100=>20
10101101=>35
10101110=>17
10101111=>7
10110000=>4
10110001=>10
10110010=>21
10110011=>15
10110100=>17
10110101=>35
10110110=>24
10110111=>12
10111000=>4
10111001=>11
10111010=>16
10111011=>13
10111100=>4
10111101=>9
10111110=>4
10111111=>2
11000000=>1
11000001=>2
11000010=>4
11000011=>3
11000100=>6
11000101=>9
11000110=>7
11000111=>3
11001000=>5
11001001=>13
11001010=>20
11001011=>12
11001100=>9
11001101=>15
11001110=>8
11001111=>3
11010000=>3
11010001=>8
11010010=>17
11010011=>12
11010100=>15
11010101=>31
11010110=>22
11010111=>11
11011000=>5
11011001=>13
11011010=>20
11011011=>16
11011100=>6
11011101=>13
11011110=>6
11011111=>3
11100000=>1
11100001=>2
11100010=>4
11100011=>3
11100100=>5
11100101=>9
11100110=>7
11100111=>4
11101000=>3
11101001=>8
11101010=>13
11101011=>11
11101100=>5
11101101=>12
11101110=>7
11101111=>4
11110000=>1
11110001=>2
11110010=>4
11110011=>3
11110100=>3
11110101=>7
11110110=>5
11110111=>4
11111000=>1
11111001=>2
11111010=>3
11111011=>3
11111100=>1
11111101=>2
11111110=>1
11111111=>1
000000000=>1
000000001=>1
000000010=>2
000000011=>1
000000100=>3
000000101=>3
000000110=>2
000000111=>1
000001000=>4
000001001=>5
000001010=>7
000001011=>3
000001100=>3
000001101=>4
000001110=>2
000001111=>1
000010000=>5
000010001=>7
000010010=>12
000010011=>5
000010100=>11
000010101=>13
000010110=>8
000010111=>3
000011000=>4
000011001=>7
000011010=>9
000011011=>5
000011100=>3
000011101=>4
000011110=>2
000011111=>1
000100000=>4
000100001=>8
000100010=>16
000100011=>7
000100100=>19
000100101=>22
000100110=>14
000100111=>5
000101000=>14
000101001=>24
000101010=>33
000101011=>15
000101100=>13
000101101=>17
000101110=>8
000101111=>3
000110000=>4
000110001=>10
000110010=>17
000110011=>9
000110100=>14
000110101=>20
000110110=>13
000110111=>5
000111000=>4
000111001=>7
000111010=>9
000111011=>6
000111100=>3
000111101=>4
000111110=>2
000111111=>1
001000000=>3
001000001=>6
001000010=>14
001000011=>6
001000100=>20
001000101=>24
001000110=>16
001000111=>6
001001000=>19
001001001=>35
001001010=>50
001001011=>23
001001100=>21
001001101=>28
001001110=>13
001001111=>5
001010000=>11
001010001=>27
001010010=>52
001010011=>27
001010100=>46
001010101=>67
001010110=>42
001010111=>15
001011000=>14
001011001=>31
001011010=>41
001011011=>23
001011100=>12
001011101=>18
001011110=>8
001011111=>3
001100000=>3
001100001=>8
001100010=>18
001100011=>11
001100100=>21
001100101=>34
001100110=>24
001100111=>9
001101000=>13
001101001=>32
001101010=>47
001101011=>27
001101100=>19
001101101=>29
001101110=>14
001101111=>5
001110000=>3
001110001=>8
001110010=>15
001110011=>11
001110100=>12
001110101=>22
001110110=>15
001110111=>7
001111000=>3
001111001=>7
001111010=>9
001111011=>6
001111100=>3
001111101=>4
001111110=>2
001111111=>1
010000000=>2
010000001=>4
010000010=>9
010000011=>4
010000100=>14
010000101=>16
010000110=>11
010000111=>4
010001000=>16
010001001=>28
010001010=>40
010001011=>18
010001100=>18
010001101=>23
010001110=>11
010001111=>4
010010000=>12
010010001=>29
010010010=>57
010010011=>29
010010100=>52
010010101=>75
010010110=>47
010010111=>17
010011000=>17
010011001=>38
010011010=>51
010011011=>28
010011100=>15
010011101=>23
010011110=>10
010011111=>4
010100000=>7
010100001=>17
010100010=>40
010100011=>22
010100100=>50
010100101=>77
010100110=>54
010100111=>20
010101000=>33
010101001=>80
010101010=>120
010101011=>67
010101100=>47
010101101=>75
010101110=>35
010101111=>13
010110000=>9
010110001=>25
010110010=>51
010110011=>34
010110100=>41
010110101=>77
010110110=>51
010110111=>22
010111000=>9
010111001=>25
010111010=>34
010111011=>24
010111100=>9
010111101=>16
010111110=>7
010111111=>3
011000000=>2
011000001=>5
011000010=>11
011000011=>7
011000100=>16
011000101=>25
011000110=>19
011000111=>7
011001000=>14
011001001=>35
011001010=>54
011001011=>31
011001100=>24
011001101=>38
011001110=>19
011001111=>7
011010000=>8
011010001=>22
011010010=>47
011010011=>32
011010100=>42
011010101=>80
011010110=>55
011010111=>24
011011000=>13
011011001=>35
011011010=>51
011011011=>35
011011100=>15
011011101=>28
011011110=>12
011011111=>5
011100000=>2
011100001=>5
011100010=>11
011100011=>8
011100100=>13
011100101=>25
011100110=>19
011100111=>10
011101000=>8
011101001=>22
011101010=>35
011101011=>27
011101100=>14
011101101=>29
011101110=>16
011101111=>7
011110000=>2
011110001=>5
011110010=>10
011110011=>8
011110100=>8
011110101=>17
011110110=>12
011110111=>8
011111000=>2
011111001=>5
011111010=>7
011111011=>6
011111100=>2
011111101=>4
011111110=>2
011111111=>1
100000000=>1
100000001=>2
100000010=>4
100000011=>2
100000100=>6
100000101=>7
100000110=>5
100000111=>2
100001000=>8
100001001=>12
100001010=>17
100001011=>8
100001100=>8
100001101=>10
100001110=>5
100001111=>2
100010000=>7
100010001=>16
100010010=>29
100010011=>14
100010100=>27
100010101=>35
100010110=>22
100010111=>8
100011000=>10
100011001=>19
100011010=>25
100011011=>13
100011100=>8
100011101=>11
100011110=>5
100011111=>2
100100000=>5
100100001=>12
100100010=>28
100100011=>15
100100100=>35
100100101=>51
100100110=>35
100100111=>13
100101000=>24
100101001=>55
100101010=>80
100101011=>42
100101100=>32
100101101=>47
100101110=>22
100101111=>8
100110000=>7
100110001=>19
100110010=>38
100110011=>24
100110100=>31
100110101=>54
100110110=>35
100110111=>14
100111000=>7
100111001=>19
100111010=>25
100111011=>16
100111100=>7
100111101=>11
100111110=>5
100111111=>2
101000000=>3
101000001=>7
101000010=>16
101000011=>9
101000100=>24
101000101=>34
101000110=>25
101000111=>9
101001000=>22
101001001=>51
101001010=>77
101001011=>41
101001100=>34
101001101=>51
101001110=>25
101001111=>9
101010000=>13
101010001=>35
101010010=>75
101010011=>47
101010100=>67
101010101=>120
101010110=>80
101010111=>33
101011000=>20
101011001=>54
101011010=>77
101011011=>50
101011100=>22
101011101=>40
101011110=>17
101011111=>7
101100000=>4
101100001=>10
101100010=>23
101100011=>15
101100100=>28
101100101=>51
101100110=>38
101100111=>17
101101000=>17
101101001=>47
101101010=>75
101101011=>52
101101100=>29
101101101=>57
101101110=>29
101101111=>12
101110000=>4
101110001=>11
101110010=>23
101110011=>18
101110100=>18
101110101=>40
101110110=>28
101110111=>16
101111000=>4
101111001=>11
101111010=>16
101111011=>14
101111100=>4
101111101=>9
101111110=>4
101111111=>2
110000000=>1
110000001=>2
110000010=>4
110000011=>3
110000100=>6
110000101=>9
110000110=>7
110000111=>3
110001000=>7
110001001=>15
110001010=>22
110001011=>12
110001100=>11
110001101=>15
110001110=>8
110001111=>3
110010000=>5
110010001=>14
110010010=>29
110010011=>19
110010100=>27
110010101=>47
110010110=>32
110010111=>13
110011000=>9
110011001=>24
110011010=>34
110011011=>21
110011100=>11
110011101=>18
110011110=>8
110011111=>3
110100000=>3
110100001=>8
110100010=>18
110100011=>12
110100100=>23
110100101=>41
110100110=>31
110100111=>14
110101000=>15
110101001=>42
110101010=>67
110101011=>46
110101100=>27
110101101=>52
110101110=>27
110101111=>11
110110000=>5
110110001=>13
110110010=>28
110110011=>21
110110100=>23
110110101=>50
110110110=>35
110110111=>19
110111000=>6
110111001=>16
110111010=>24
110111011=>20
110111100=>6
110111101=>14
110111110=>6
110111111=>3
111000000=>1
111000001=>2
111000010=>4
111000011=>3
111000100=>6
111000101=>9
111000110=>7
111000111=>4
111001000=>5
111001001=>13
111001010=>20
111001011=>14
111001100=>9
111001101=>17
111001110=>10
111001111=>4
111010000=>3
111010001=>8
111010010=>17
111010011=>13
111010100=>15
111010101=>33
111010110=>24
111010111=>14
111011000=>5
111011001=>14
111011010=>22
111011011=>19
111011100=>7
111011101=>16
111011110=>8
111011111=>4
111100000=>1
111100001=>2
111100010=>4
111100011=>3
111100100=>5
111100101=>9
111100110=>7
111100111=>4
111101000=>3
111101001=>8
111101010=>13
111101011=>11
111101100=>5
111101101=>12
111101110=>7
111101111=>5
111110000=>1
111110001=>2
111110010=>4
111110011=>3
111110100=>3
111110101=>7
111110110=>5
111110111=>4
111111000=>1
111111001=>2
111111010=>3
111111011=>3
111111100=>1
111111101=>2
111111110=>1
111111111=>1
0000000001=>1
0010000001=>6
0010101101=>96
0010101011=>87
0010100111=>27
0010011101=>30
0010011011=>37
0010010111=>23
0010001111=>6
0001110101=>22
0001110011=>11
0001101101=>29
0001101011=>27
0001100111=>9
0001011101=>18
0001011011=>23
0001010111=>15
0001001111=>5
0000111101=>4
0000111011=>6
0000110111=>5
0000101111=>3
0000011111=>1
0000000000=>1
0000000110=>2
0000011000=>4
0000011110=>2
0000010010=>12
0001100000=>4
0001100110=>26
0001111000=>4
0001111110=>2
0001110010=>17
0001001000=>24
0001001110=>14
0001000010=>18
0001011010=>43
0010101010=>169
0010101000=>53
0010101100=>67
0010100100=>78
0010010100=>78
0001010100=>53
0010101110=>44
0010100000=>11
0010000100=>22
0000010100=>11
0000000010=>2
0000001110=>2
0000111110=>2
0000000100=>3
0000001010=>7
0000010110=>8
0000101110=>8
0001011110=>8
0001101110=>14
0001110110=>15
0001111010=>9
0001111100=>3
0000000101=>3
0000001101=>4
0000011101=>4
0001111101=>4
0000001001=>5
0000010101=>13
0000101101=>17
0010110001=>39
0001100001=>11
0001000001=>8
0000111111=>1
0001110100=>14
0001101100=>21
0010011100=>21
0001011100=>13
0000111100=>3
0001101010=>51
0010011010=>71
0000111010=>9
0010100110=>77
0010010110=>66
0001010110=>44
0000110110=>13
0010001110=>16
0001101001=>36
0000110001=>10
0000010001=>7
0000001100=>3
0000011001=>7
0000110011=>9
0000110100=>14
0000000011=>1
0000011011=>5
0001101111=>5
0000110101=>20
0010000010=>14
0001000011=>8
0010011110=>13
0001010000=>15
0001000100=>25
0001010101=>71
0001001011=>25
0001100011=>13
0001110111=>7
0010000000=>3
0000000111=>1
0000001111=>1
0001111111=>1
0000001011=>3
0000010111=>3
0001011111=>3
0001111001=>7
0000011010=>9
0000101010=>33
0000100101=>22
0010010001=>45
0010000101=>25
0010010101=>107
0010010011=>42
0000101011=>15
0001000111=>7
0000100111=>5
0010010010=>86
0001001010=>57
0001001001=>41
0001000101=>29
0000100011=>7
0000100100=>20
0000100010=>17
0010110000=>14
0000011100=>3
0000001000=>4
0000101100=>13
0010101111=>15
0000101000=>15
0010001000=>25
0001001100=>24
0001000110=>19
0001100100=>26
0001100010=>23
0000100110=>14
0000110010=>17
0010010000=>20
0001010010=>60
0001000000=>4
0001011001=>33
0001100101=>38
0001110001=>10
0010011001=>54
0010100101=>113
0010101001=>117
0010011111=>5
0000111001=>7
0010001101=>34
0001001101=>30
0001010001=>33
0001010011=>29
0001111011=>6
0010011000=>26
0001011000=>17
0000100000=>5
0010001011=>27
0010000111=>6
0000010011=>5
0010001100=>27
0010000110=>17
0000110000=>5
0000100001=>9
0010100011=>34
0010100001=>28
0000111000=>4
0001101000=>17
0000010000=>5
0000101001=>24
0010100010=>64
0010001001=>43
0010000011=>6
0010001010=>61
0001110000=>4
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The number of standard Young tableaux whose descent set is the binary word.
A descent in a standard Young tableau is an entry $i$ such that $i+1$ appears in a lower row in English notation.
For example, the tableaux $[[1,2,4],[3]]$ and $[[1,2],[3,4]]$ are those with descent set $\{2\}$, corresponding to the binary word $010$.
A descent in a standard Young tableau is an entry $i$ such that $i+1$ appears in a lower row in English notation.
For example, the tableaux $[[1,2,4],[3]]$ and $[[1,2],[3,4]]$ are those with descent set $\{2\}$, corresponding to the binary word $010$.
Code
def statistic(w): D = [i+1 for i in range(len(w)) if w[i]==1] return len([T for T in StandardTableaux(len(w)+1) if T.standard_descents() == D])
Created
Jun 15, 2017 at 08:07 by Martin Rubey
Updated
Jun 15, 2017 at 08:07 by Martin Rubey
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